Question

Findhevalueofkif(x-1)isafactorof4x3+3x2-4x+k.​

Answer 1

✬ The value of k is -3✬

Step-by-step explanation:

$\\ \underline{ \bigstar \: \boldsymbol{Appropriate\;Question:}}$

• Find the value of k if (x - 1) is a factor of 4x³ + 3x² - 4x + k.

Given equation: f(x) = 4x³ + 3x² - 4x + k

To find: Value of k

Where,

• x - 1 = 0 → x = 1

Putting the value of x in the equation,

$\\ \longmapsto\sf{f(x) = 4 {x}^{3} + 3 {x}^{2} - 4x + k } \\ \\ \longmapsto\sf{f(1) = 4 {(1)}^{3} + 3 {(1)}^{2} - 4(1) + k} \\ \\ \longmapsto\sf{f(1) = 4 + 3 - 4 + k} \\ \\ \longmapsto\sf{f(1) = 3 + k} \\ \\ \longmapsto \underline{ \boxed{\frak{ - 3 = k}}} \: \green{ \bigstar}$

• Hence,the value of k is -3.

Answer 2

Answer:

Required Answer:-

let's understand the concept:-

Here if x-1 is a factor of the the polynomial =>x-1=0=>x=1

If it is a factor then p (1)=0

solution:-

$\sf {p (x)={4x}^{2}+{3x}^{2}-4x+k}p(x)=4x$

${:}\dashrightarrow:⇢ \sf {p(x)={7x}^{2}-4x+k}$

According to the question

${:}\dashrightarrow:⇢ p (1)=0p(1)=0$

${:}\dashrightarrow:⇢ 7 (1){}^{2}-4 (1)$

${:}\dashrightarrow:⇢ 7×1-4+k=07×1−4+k=0$

${:}\dashrightarrow:⇢ 7-4+k=07−4+k=0$

${:}\dashrightarrow:⇢ 3+k=03+k=0$

${:}\dashrightarrow:⇢ {\underline{\boxed{\bf {k=(-3)}}}}$

$\therefore∴ \sf {The\:value\:of\:k=(-3)}$